2 Answers
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The issue would seem to be one of muktza - objects that may not be moved during shabas because they are not for shabas use. Let us assume that a standard watch is not muktza because it is a k'li shem'lachto l'heter - its normal usage is permitted on shabas. (See the last line of the long paragraph on this convenient Google hit.)

The complex devices to which you refer have this functionality as well as some other functionality. If the additional functionality were to prohibit the otherwise permissible watch, it must be because we assess those functions separately, as if it were a hybrid between a watch and [for example] a remote control. The latter would be a k'li shem'lachto l'isur - a tool whose normal usage is prohibited on shabas, which is consequently immovable barring special circumstances. If so, we have a case of one muktza object inextricably attached to one non-muktza object, which is addressed by Ramba"m in his Hilchos Shabas 25:14,15. He says that moving the assemblage for the permissible item is permitted while moving it for the prohibited item is prohibited.

The above makes the assumption that anything strapped to the wrist that has a clock face is defined as a watch regardless of its other accessories.

(The other exceptional case you mentioned - an especially elegant watch that is considered jewelry - might actually present an unrelated muktza problem, which is concern for chisaron kis - monetary loss. Very expensive objects are muktzim as well.)

At what point does the concern for Ḥisaron Kis overtake and overwhelm Kavod Shabbath? If one wears a diamond-crusted watch only on Shabbath out of Kavod, is that problematic, because the watch is worth several thousand dollars and carries its own insurance policy? What if it's not diamond-encrusted but made by a very prestigious company and still retains a very high value? What if this is in a wealthy community and the wearer is also sporting diamond-crusted cufflinks and a platinum belt buckle? Where is the line drawn?
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Seth JDec 12 '11 at 15:54

WAF, not to toot my own horn at all, but see this answer (judaism.stackexchange.com/a/12168/5) regarding Muktzeh MeḤamath Ḥisaron Kis. Merely being very valuable does not make a watch Muktzeh. To be Muktzeh, an object of great value would have to be used for something specific that one would not dare to use for any other purpose for fear of damaging it (special knife for a butcher); set aside specifically to avoid being used ever for fear of damaging it (collectibles, antiques, etc.); or merchandise, even Melachto LeHeter, that one wouldn't want to damage lest it become unsellable.
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Seth JDec 12 '11 at 19:08

I would think to say from this daily Halacha that any watch that simply has the date/time is fine, but when you start to get involved with those "tv watches" there probably would be a problem because the watch is only a "tafel" to the tv. This is one of those serious cases of CYLOR